Health professionals extensively use Two-Dimensional (2D) Ultrasound (US) videos and images to visualize and measure internal organs for various purposes including evaluation of muscle architectural changes. US images can be used to measure abdominal muscles dimensions for the diagnosis and creation of customized treatment plans for patients with Low Back Pain (LBP), however, they are difficult to interpret. Due to high variability, skilled professionals with specialized training are required to take measurements to avoid low intra-observer reliability. This variability stems from the challenging nature of accurately finding the correct spatial location of measurement endpoints in abdominal US images. In this paper, we use a Deep Learning (DL) approach to automate the measurement of the abdominal muscle thickness in 2D US images. By treating the problem as a localization task, we develop a modified Fully Convolutional Network (FCN) architecture to generate blobs of coordinate locations of measurement endpoints, similar to what a human operator does. We demonstrate that using the TrA400 US image dataset, our network achieves a Mean Absolute Error (MAE) of 0.3125 on the test set, which almost matches the performance of skilled ultrasound technicians. Our approach can facilitate next steps for automating the process of measurements in 2D US images, while reducing inter-observer as well as intra-observer variability for more effective clinical outcomes.